Curran, 23, sustained the injury while playing for Chennai Super Kings in the Indian Premier League (IPL) on Saturday and will return to Britain for further scans.
Tom Curran, named as a reserve in England's 15-man preliminary squad, will replace his brother Sam, while bowler Reece Topley will join the group as a travelling reserve.
"The England players and management not at the IPL arrived at their Muscat base earlier today and will remain in Oman until 16 October before moving to Dubai for the start of the tournament," the statement said.
The T20 World Cup will be held from Oct 17 to Nov 14 in the United Arab Emirates and Oman. England take on defending champions West Indies in their opener on Oct. 23 in Dubai.